|Most mboards require you connect both the main 20 or 24 pin connector and a smaller connector from the PS to sockets on the mboard. .|
I'm assuming you connected both.
You could try this - if you get no beeps, the mboard is probably definitely dead - it was probably damaged by the BESTEC PS.
Make sure you have a speaker or speakers or the equivalent connected to the mboard so you can hear mboard beeps (see your mboard manual if you need to).
Remove the AC power to the case/power supply.
Remove all the ram.
Restore AC power.
Try to boot.
If nothing else is wrong, you will get no video but you will hear a pattern of beeps that indicate no ram is installed, or a ram problem.
E.g. for an Award bios or a bios based on one, that's often a beep of about a half second, silence for a half second, a beep of about a half second, silence for a half second, continuously.
If you still get no beeps .....
What you do now is up to you.
Your're going to need to risk spending up to $200 to fix the system, if you don't have a used PS and a used suitable mboard already.
Although, if you get a PS with, say, 650watts capacity, you can always use it for a new custom generic system with just about any graphics card installed in a slot on it.
If you replace the power supply and the mboard, the chances are quite good that your system will then work fine, but that's not 100% certain. .
I can look up which specific mboard you have (the TriGem company that made the emachines computer probably didn't make the mboard) , and see if there are used ones with an emachines bios version available on the web.
You can use any mboard that is compatible with your cpu and ram, but you probably won't be able to restore the original emachines software installation by using Recovery disks for your specific model unless the model detected by the program is deemed acceptable by the installation program and the mboard has an emachines bios version.
Apparently emachines systems don't come with Recovery disks, but there is a program already on the computer when you get it with which you can make them yourself while Windows and the computer are working fine.
Or, if your model is not more than about 5 years old, they can probably be ordered from the emachines web site. If can get them, the cost is probably much less than for a Vista DVD alone.
If you get another desktop emachines system, there's nothing especially inferior about them except for the PS - if the PS is BESTEC, I recommend you take it out and install a better PS.